Express $71 \frac{1}{2} %$ As A Fraction In Simplest Form.A) 3 80 \frac{3}{80} 80 3 ​ B) 3 800 \frac{3}{800} 800 3 ​ C) 3 100 \frac{3}{100} 100 3 ​

Understanding the Problem

Expressing a mixed number as a fraction is a fundamental concept in mathematics that requires a clear understanding of fractions and their conversion. In this article, we will focus on expressing the mixed number $71 \frac{1}{2} \%$ as a fraction in simplest form.

What is a Mixed Number?

A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number and $\frac{b}{c}$ is the fraction. In the given problem, $71 \frac{1}{2} \%$ is a mixed number where $71$ is the whole number and $\frac{1}{2}$ is the fraction.

Converting a Mixed Number to a Fraction

To convert a mixed number to a fraction, we need to follow these steps:

1. Multiply the whole number by the denominator: Multiply the whole number by the denominator of the fraction.
2. Add the numerator: Add the numerator of the fraction to the product obtained in step 1.
3. Write the result as a fraction: Write the result obtained in step 2 as a fraction with the denominator.

Applying the Steps to the Given Problem

Let's apply the steps to the given problem:

1. Multiply the whole number by the denominator: Multiply $71$ by $2$ (the denominator of $\frac{1}{2}$).
2. Add the numerator: Add $1$ (the numerator of $\frac{1}{2}$) to the product obtained in step 1.
3. Write the result as a fraction: Write the result obtained in step 2 as a fraction with the denominator.

The result of step 1 is $142$. The result of step 2 is $143$. Therefore, the fraction equivalent of $71 \frac{1}{2} \%$ is $\frac{143}{2}$.

Simplifying the Fraction

To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of $143$ and $2$ is $1$. Since the GCD is $1$, the fraction $\frac{143}{2}$ is already in its simplest form.

Conclusion

In conclusion, the mixed number $71 \frac{1}{2} \%$ can be expressed as a fraction in simplest form as $\frac{143}{2}$. This is the final answer to the problem.

Answer Options

The answer options provided are:

A) $\frac{3}{80}$ B) $\frac{3}{800}$ C) $\frac{3}{100}$

However, none of these options match the correct answer, which is $\frac{143}{2}$.

Why the Other Options are Incorrect

The other options are incorrect because they do not match the correct answer. Option A is incorrect because the numerator is $3$, not $143$. Option B is incorrect because the denominator is $800$, not $2$. Option C is incorrect because the numerator is $3$, not $143$.

Final Thoughts

Frequently Asked Questions

In this article, we will address some of the most frequently asked questions related to expressing a mixed number as a fraction.

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number and $\frac{b}{c}$ is the fraction.

Q: How do I convert a mixed number to a fraction?

A: To convert a mixed number to a fraction, you need to follow these steps:

1. Multiply the whole number by the denominator: Multiply the whole number by the denominator of the fraction.
2. Add the numerator: Add the numerator of the fraction to the product obtained in step 1.
3. Write the result as a fraction: Write the result obtained in step 2 as a fraction with the denominator.

Q: What if the denominator is not 1?

A: If the denominator is not 1, you need to multiply the whole number by the denominator and then add the numerator. For example, if you have the mixed number $3 \frac{1}{4}$, you would multiply $3$ by $4$ to get $12$, and then add $1$ to get $13$. The result is $\frac{13}{4}$.

Q: Can I simplify the fraction after converting it?

A: Yes, you can simplify the fraction after converting it. To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator. If the GCD is greater than 1, you can divide both the numerator and the denominator by the GCD to simplify the fraction.

Q: What if the GCD is 1?

A: If the GCD is 1, the fraction is already in its simplest form. You do not need to simplify it further.

Q: Can I convert a mixed number to a decimal?

A: Yes, you can convert a mixed number to a decimal. To convert a mixed number to a decimal, you need to divide the numerator by the denominator. For example, if you have the mixed number $3 \frac{1}{4}$, you would divide $13$ by $4$ to get $3.25$.

Q: What if I have a mixed number with a negative whole number?

A: If you have a mixed number with a negative whole number, you need to follow the same steps as before. However, you need to be careful when multiplying the whole number by the denominator. For example, if you have the mixed number $-3 \frac{1}{4}$, you would multiply $-3$ by $4$ to get $-12$, and then add $1$ to get $-11$. The result is $\frac{-11}{4}$.

Q: Can I convert a mixed number to a percentage?

A: Yes, you can convert a mixed number to a percentage. To convert a mixed number to a percentage, you need to divide the numerator by the denominator and then multiply by 100. For example, if you have the mixed number $3 \frac{1}{4}$, you would divide $13$ by $4$ to get $3.25$, and then multiply by 100 to get $325\%$.

Conclusion

In conclusion, expressing a mixed number as a fraction requires a clear understanding of fractions and their conversion. We have provided a step-by-step guide on how to convert a mixed number to a fraction, and we have also addressed some of the most frequently asked questions related to this topic.